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Additionally to Peter Crooks answer I would recommend to study the book of Hotta and others : D-Modules, Perverse Sheaves, and Representation Theory Here you can learn about derived categories and pe …

My question is simple: Given an algebraic group $G$ acting on a variety $X$ algebraically. If the orbits are of finite number then they form what is called an algebraic stratification of $X$. Now my …

Geometric respectively topological methods are widely applied in representation theory. As far as I know mainly cohomological methods are used. I wonder if there are concrete applications of the …

Let $G$ be a complex reductive group, $L\subset G$ a Levi subgroup and $Rep(G)$ the category of rational representations of $G$. My Question: What is the geometric analogue of the restriction f …

One can also argue as follows: $G(\mathcal{O})$ operates transitivly on each stratum $\mathcal{G}^\lambda$. The isotropy group at $t^\lambda$ is $P^a_\lambda:= (t^\lambda)^{-1}G(\mathcal{O})t^\lambda …

The point is following: $\overline{Gr^\lambda}$ is a finite dimensional variety acted upon by the pro-algebraic group $G(\mathbb{C}[[t]])$. This action factors through the action of some finite dim …

Let $G$ be an algebraic group (over $\mathbb{C}$) acting algebraically on a variety $X$. Bernstein and Lunts then define in [BL94] the equivariant derived category $D^b_G(X,\mathbb{C})$ (of $\mathbb{C …

I hope this is not too elementary! Let $G$ be a algebraic reductive group over $\mathbb{C}$. The group $G(\mathbb{C}[[t]])$ can be given the structure of a pro algebraic group as follows. Let $l\in …

This question is closely related to Peter Crooks question. Strata of the Affine Grassmannian Let $G$ be a complex reductive group, $\mathcal{K}:= \mathbb{C}((t))$, $\mathcal{O}:= \mathbb{C}[[t]]$ and …

So Ulrich and Geordie were right, Tom Braden was the right person to ask and here is what he told me: The answer is yes, in the case above $X$ is Whitney stratified. The argument goes roughly as fol …

So i turned my comment into an answer after reading [1] again. A Whitney stratification, i.e. a stratification satisfying Whitney's condition b (and so automaticly a), induces a triangulation compati …

I do not really answer you question but maybe this helps: Let $\mathcal{K} =\mathbb{C}((t))$ and $\mathcal{O}:=\mathbb{C}[[t]]$. For $n\geq 0$ denote the $\mathcal{K}_n$ the $\mathcal{O}$ ideal in $\ …

Setup: Let $\mathcal{K}=\mathbb{C}((t))$, $\mathcal{O}:= \mathbb{C}[[t]]$ and $G$ be a reductive algebraic group (over $\mathbb{C}$). Let further $\mathcal{K}_n$ denote the $\mathcal{O}$-ideal in $\m …

I hope this question is not too vague. Let $G$ be a complex reductive group, $B$ a Borel subgroup of $G$, and $P$ a parabolic containing $B$. Denote by $\pi:G/B\to G/P$ the canonical map. Consider th …

I do this all over $\mathbb{C}$. By [BBD] this should not be a problem. Assume $X=\mathbb{C}P^1$, $U=\mathbb{C}$, $S_1= U$, $S_0=X-U$. Let further $j_i:S_i\hookrightarrow X$ be the inclusion maps. Th …